**Abstract**

The universal principles of fluid motion are the conservation of mass, momentum and energy. This chapter will introduce the CFD governing equations and describe how the continuity equation, component equation, Navier-Stokes equation and energy equation were derived from the principles above. With the expanding application of CFD simulation technology, some processes such as fluid-involved reactions, adsorption and permeation, which break the conservation of mass, momentum and energy for fluid phase, should be coupled to CFD model. In view of this, this chapter provided the theories about source terms for the mass equation, momentum equation and thermal energy equation. The technology for solving these governing equations remained a challenge for a long period due to the complexity. Thanks to the development of numerical methods, such as the finite difference method and the finite volume method, these equations can be solved and provide reasonable numerical results of flows, heat transfer and reactions. This chapter also demonstrates the basics of these two major numerical techniques.

**Keywords:** governing equations, finite-difference method, finite-volume method, reacting flow, multiphase flow, source term
